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Solving ODEs with Mathematica
Solving ODEs with Mathematica

...  Purpose: Mathematica solves difficult mathematical formulas  Focus: solving ordinary differential equations (ODEs) of 1st and higher order using Mathematica dy 1st Order ODE:  f ( x, y ) dx dzx Higher Order ODE:  f ( x, y ) z dy ...
Incremental temporal reasoning in job shop scheduling repair Please share
Incremental temporal reasoning in job shop scheduling repair Please share

... will take too much unnecessary time to traversal the nodes until one of them is less than -nC, where n denotes the number of the nodes and C denotes the largest absolute value of some arc length. For example, in a 10 jobs, 10 machines job shop problem, there are more than 200 nodes and the largest a ...
Learning Distinctions and Rules in a Continuous World through
Learning Distinctions and Rules in a Continuous World through

... than it would otherwise. It will then create a rule of the form r1 = hux→(0, ∞) ⇒ ḣx→(0, ∞)i. In the simulator it takes a force of 300 to move the hand. By noting the real value ũx each time event ux→(0, ∞) occurs, the agent can use the occurrence or nonoccurrence of event ḣx →(0, ∞) as a supervi ...
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2-2

... This equation contains multiplication and addition. Equations that contain two operations require two steps to solve. Identify the operations in the equation and the order in which they are applied to the variable. Then use inverse operations to undo them in reverse over one at a time. Operations in ...
Notes on the ACL2 Logic
Notes on the ACL2 Logic

Solving Distributed Constraint Optimization Problems Using Logic
Solving Distributed Constraint Optimization Problems Using Logic

... to coordinate their value assignments to maximize the sum of resulting constraint utilities [33, 37, 31, 46]. Researchers have used them to model various multi-agent coordination and resource allocation problems [30, 48, 49, 25, 23, 43, 27]. The field has matured considerably over the past decade, a ...
Theorem provers an overview
Theorem provers an overview

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Exact Algorithms via Monotone Local Search
Exact Algorithms via Monotone Local Search

... n/2. Indeed, for k sufficiently far away from n/2, trying all subsets of size k takes time k n which is significantly faster than O(2n ). Thus, if there is an algorithm deciding whether there is a solution of size at most k in time ck nO(1) for some c < 4, we can deduce that the problem can be solve ...
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Optimal Allocation Strategies for the Dark Pool Problem

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Study on Selection of Intelligent Waterdrop Algorithm for

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Dilemma First Search for Effortless Optimization of NP-hard
Dilemma First Search for Effortless Optimization of NP-hard

... information can be leveraged. First, if the computational resources are limited to computing a single candidate solution, then computing the greedy solution yields the best chances of obtaining the optimal solution. Moreover, from Theorem 2 and Eq. (2), altering high-quality sets of solutions is exp ...
UTEP - The University of Texas at El Paso
UTEP - The University of Texas at El Paso

... The slope of a line refers to the slant or inclination of the line. The slope is the ratio of the vertical change to the horizontal change between two points on the line. The slope can also be called the rise over run ratio because it tells how many spaces to move up or down and how many spaces to m ...
Solving Distributed Constraint Optimization Problems Using Logic
Solving Distributed Constraint Optimization Problems Using Logic

... them. In our DCOP example, agent a3 computes the optimal utility for each value combination of variables x1 and x2 (see Table 1(a)), and sends the utilities to its parent agent a2 in a UTIL message. For example, consider the first row of Table 1(a), where x1 = 0 and x2 = 0. The variable x3 can be as ...
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Dynamic Programming and Graph Algorithms in Computer Vision

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Improved Memory-Bounded Dynamic Programming for

... top-down heuristics. For every identified belief state bt at horizon t the best joint policy is added. Additionally, in step two the set of most likely observations for every agent is identified, bounded by a pre-defined number of observations maxObs. More specifically, for the most likely belief st ...
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Probably Approximately Correct Heuristic Search

... Search (Thayer and Ruml 2008) are known examples of w-admissible algorithms. In general, w-admissible search algorithms achieve w-admissibility by using an admissible heuristic to obtain a lower bound on the optimal solution. When the ratio between the incumbent solution (i.e., the best solution fou ...
Lesson 2: Intersecting Two Lines, Part One
Lesson 2: Intersecting Two Lines, Part One

... Commons License (specifically agreement # 3 “attribution and non-commercial.”) Until such time as the document is completed, however, the author reserves all rights, to ensure that imperfect copies are not widely circulated. ...
PDF
PDF

... point in the search. The current assignments of these variables may or may not correspond to the assignments specified in the label. Definition 3. A label, λ, is valid iff every variable assignment hx = ai ∈ λ is the current assignment of the variable x. During search we will induce nogoods, i.e. pa ...
The Intelligence of Dual Simplex Method to Solve Linear Fractional
The Intelligence of Dual Simplex Method to Solve Linear Fractional

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Unification (computer science)

Unification, in computer science and logic, is an algorithmic process of solving equations between symbolic expressions.Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactical unification, otherwise semantical, or equational unification, or E-unification, or unification modulo theory.A solution of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a complete, and minimal substitution set, that is, a set covering all its solutions, and containing no redundant members. Depending on the framework, a complete and minimal substitution set may have at most one, at most finitely many, or possibly infinitely many members, or may not exist at all. In some frameworks it is generally impossible to decide whether any solution exists. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.For example, using x,y,z as variables, the singleton equation set { cons(x,cons(x,nil)) = cons(2,y) } is a syntactic first-order unification problem that has the substitution { x ↦ 2, y ↦ cons(2,nil) } as its only solution.The syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms; however, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite trees.The semantic first-order unification problem { a⋅x = x⋅a } has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative; the same problem, viewed in an abelian group, where (⋅) is considered also commutative, has any substitution at all as a solution.The singleton set { a = y(x) } is a syntactic second-order unification problem, since y is a function variable.One solution is { x ↦ a, y ↦ (identity function) }; another one is { y ↦ (constant function mapping each value to a), x ↦ (any value) }.The first formal investigation of unification can be attributed to John Alan Robinson, who used first-order syntactical unification as a basic building block of his resolution procedure for first-order logic, a great step forward in automated reasoning technology, as it eliminated one source of combinatorial explosion: searching for instantiation of terms. Today, automated reasoning is still the main application area of unification.Syntactical first-order unification is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms.Semantic unification is used in SMT solvers and term rewriting algorithms.Higher-order unification is used in proof assistants, for example Isabelle and Twelf, and restricted forms of higher-order unification (higher-order pattern unification) are used in some programming language implementations, such as lambdaProlog, as higher-order patterns are expressive, yet their associated unification procedure retains theoretical properties closer to first-order unification.
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